While markets are often decentralized, in many other cases
agents in one role can only negotiate with a proper subset
of the agents in the complementary role. There may be proximity
issues or restricted communication flows. For example,
information may be transmitted only through word-of-mouth,
as is often the case for job openings, business opportunities,
and confidential transactions. Bargaining can be considered
to occur over a network that summarizes the structure of
linkages among people. We conduct an alternating-offer
bargaining experiment using separate simple networks, which
are then joined during the session by an additional link.
The results diverge sharply depending on how this connection
is made. Payoffs can be systematically affected even for
agents who are not connected by the new link. We use a
graph-theoretic analysis to show that any two-sided network
can be decomposed into simple networks of three types, so
that our result can be generalized to more complex bargaining
environments. Participants appear to grasp the essential
characteristics of the networks and we observe a rather
consistently high level of bargaining efficiency.